Abstract: The exact distribution of the
square sum of Dirichlet random variables is given by two different univariate
integral representations. Alternatively, three representations by orthogonal
series with Jacobi or Legendre polynomials are derived. As a special case, the
distribution of the square sum of spacings - also called
Greenwood
’s statistic - is obtained. Nine quantiles of are tabulated with eight digits for n
from 10 to 100.
Keywords and phrases: Greenwood’s statistic, square sum of spacings, Dirichlet distribution, distribution of the sample coefficient of variation from gamma random variables, exact distributions, tabulated quantiles, goodness of fit tests, tests for exponentiality, tests for gamma distributions.
